Since the violent relaxation in hierarchical merging is incomplete, elliptical galaxies retain a wealth of information about their formation pathways in their present-day orbital structure. A variety of evidence indicates that gas-rich major mergers play an important role in the formation of elliptical galaxies. We simulate 1:1 disk mergers at seven different initial gas fractions ranging from 0 to 40%, using the TreeSPH code Gadget-2. We classify the stellar orbits in each remnant and construct radial profiles of the orbital content, intrinsic shape, and orientation. The dissipationless remnants are typically prolate-triaxial, dominated by box orbits within r_c ~ 1.5Reff, and by tube orbits in their outer parts. As the gas fraction increases, the box orbits within r_c are increasingly replaced by a population of short axis tubes (z-tubes) with near zero net rotation, and the remnants become progressively more oblate and round. The long axis tube (x-tube) orbits are highly streaming and relatively insensitive to the gas fraction, implying that their angular momentum is retained from the dynamically cold initial conditions. Outside r_c, the orbital structure is essentially unchanged by the gas. The 15-20% gas remnants often display disk-like kinematically distinct cores (KDCs). These remnants show an interesting resemblance, in both their velocity maps and intrinsic orbital structure, to the KDC galaxy NGC4365 (van den Bosch et al. 2008). At 30-40% gas, the remnants are rapidly rotating, with sharp embedded disks on ~ 1Reff scales. We predict a characteristic, physically intuitive orbital structure for 1:1 disk merger remnants, with a distinct transition between 1 and 3Reff that will be readily observable with combined data from the 2D kinematics surveys SAURON and SMEAGOL.
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